A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
An object, such as a stage of a lithographic apparatus, may in use exhibit non rigid body mass behavior. In particular, this may be the case in situations where the object is subjected to high forces, for example in order to move the object with high velocity and acceleration. An example of such non rigid body mass behavior is torsion. In a measurement system that measures a position of the object, a plurality of position sensors are connected to the object spaced apart from each other, position information from two or more position sensors may be applied. In a lithographic apparatus, an example of such a configuration may be found in stage position measurement, e.g. substrate table position measurement or support (e.g. mask table) position measurement. A plurality of sensors (e.g. encoders, interferometers) are provided in order to measure a vertical (and or horizontal) position of the stage. The multiple vertical position measurements may be applied to calculate a vertical translation (Z) and 1 or 2 tilt rotations (Rx, Ry) about horizontal axis (y respectively x-axis) of the stage. A torsion mode of the stage seen in the vertical or tilt open loop mechanics—may therefore result in differences in the readout of the position sensors, as during excitation of such torsion modes, vertical displacement of parts of the stage may occur. If the stage is positioned in the horizontal plane, the vertical dynamics may show different amplification of the torsion mode at different horizontal positions. In order to reduce an effect of such torsion mode excitations on e.g. closed loop position control loop behavior, several solutions have been devised. Firstly, a bandwidth of the loop may be kept relatively low, which however has adverse effects on speed, accuracy of positioning, etc. Secondly, notch filters may be applied in order to reduce frequency components of the sensor signals in a frequency range where the excitation of the torsion mode resides. Advanced control solutions are considered to require complex calculations (e.g. position dependent Notch filters) and therefore impose a high data processing load in the lithographic apparatus.